1. Field of the Invention
The present invention relates generally to the field of data acquisition and signal processing systems, and more particularly to AC calibration methods which account for a system's transfer chacteristics by utilizing bilevel signal patterns as test signals for determining the system's transfer function.
2. Description of the Prior Art
Typically, a data acquisition system (DAS) is composed of one or more analog input channels, an analog-to-digital converter (ADC), arithmetic, amplification, and filter systems (referred to as processing systems), and either digital outputs or a digital-to-analog converter (DAC) and analog outputs. AC calibration of the system is required to account for the transfer characteristics of the ADC, processing systems and/or DAC, i.e., the system's response to particular inputs. Only an initial AC calibration of the DAS is performed, and for most systems, generalized transfer functions can be derived for any arbitrary input waveform.
Typically, AC calibration of a DAS involves parallel computation of calibration coefficients by simultaneously observing both the stimulus and response for the system. The calibration adjustment may be either post-processing or, by feedback loop, pre-processing to the DAS.
It is assumed that systems of the type under concern are approximately linear. The input and output of such a system is related by a linear differential equation with constant coefficients, for example: ##EQU1## where a.sub.0, a.sub.1, . . . b.sub.0, b.sub.1, . . . are constants.
The frequency transfer function, H(.omega.), for this system is defined as: ##EQU2## where X(.omega.) is the Fourier transform of the input function x(t), and Y(.omega.) is the Fourier transform of the response function y(t).
Thus, a common method for testing the DAS is to apply to the input(s) of the DAS a sinusoidal pattern. The output will be a second sinusoid having a different amplitude, and usually a different phase, but the same frequency, as the input sinusoid. The above ratio then yields values in terms of amplitude and phase of the system frequency transfer function at that frequency. This data can then be used to generate a correction coefficient vector for the signal processing system. Thus, determining the frequency transfer function for a system is an integral step in AC calibration of that system.
Correction coefficients can be determined by the method detailed above only one frequency at a time. This process is slow, limits exact correction to those frequencies tested, thereby producing only approximate correction for other frequencies in the bandwidth, and is subject to the added errors of inaccuracy of frequency selection devices.
A modified approach utilizing this principal is to apply an impulse, such as a delta function, to the system. The width of the impulse, .tau., of a true delta function is vanishingly small. This implies that the impulse must have a very large amplitude in order to generate sufficient response energy to maintain a high signal to noise ratio. The practical limits on generating such an impulse, including rise and decay times of the signal generator, maximum input range of the system, etc., yields generating and/or utilizing such an actual impulse impracticable.
There is a present need in the art for a broadband method of determining the absolute frequency transfer function of a signal processing system for AC signals and AC signals having DC components which is faster and more independent of other device errors than the presently existing methods.